Subject: Re: two cylces From: "Pennington, Mark" <mwpennin@xxxxxxxx> Date: Mon, 6 Nov 2006 17:23:17 -0500Dick, Thank you very much for your useful comments. I had considered the running method, but was greatly concerned about the properties of the normalized running product, which is important since I'm using the value of the normalized peak ACF as a cue for modulation noise. I had searched the literature, but wasn't able to find a full discussion on the normalization of the running product, though it's certainly possible I might have missed something. So I decided to play it safe and use the most well-known and straightforward implementation of the ACC (p. 98), despite its shortcomings. All the same, it fared pretty well as far as gross pitch errors are concerned, when compared to the ESPS method (in WaveSurfer, see Table 5.2, p. 116). Mark Mark, I think what you're showing is that applying a rectangular window and then computing an ACF of the windowed signal is a poor way to use the ACF concept, since it can severely degrade the "repetition" property that you're looking for. Especially if the window is too short, as R&S show. If instead you use the "running" method, of applying an LPF to the running product of a signal with a delayed version of itself, with no need for windowing, simple peak picking will work much more robustly. This is what Licklider proposed in 1952 in his "Duplex model of pitch perception". R&S's window condition should not be taken the be the same as the psychophsical result that two cycles of a waveform are sufficient to hear a pitch. Dick [Hide Quoted Text] Dear List, Rabiner and Schafer (1978: 145, Digital Processing of Speech Signals) state that "to get any indication of periodicity in the autocorrelation function, the window must have a duration of at least two periods of the waveform." Using an autocorrelation (ACC) function with a 39.37 ms rectangular window, I tested this proposition with three 2.5 s sawtooth waves at 27.5 Hz (pitch period = 36.36 ms), 38.9 Hz (25.71 ms), and 55 Hz (18.18 ms). R&S's statement holds if the ACC function is scanned for its maximum value. Only the F0 of the 55 Hz sawtooth is accurately determined (mean calculated over the 2.5 s waveform = 54.74 Hz). The other F0s are severely overestimated, the mean estimated F0s of the 27.5 and 38.9 Hz sawtooths being respectively 281.19 and 179.54 Hz. Because two periods of the 55 Hz sawtooth are equal to 36.36 ms, R&S are clearly correct if the ACC maximum value detection method is employed, given the 39.37 ms rectangular window. On the other hand, using the ACC peak-peaking method developed in Section 4.2.2 of my thesis (p. 96-98), I found that the respective mean F0s of the 27.5, 38.9, and 55 Hz sawtooths to be 31.52, 41.30, and 54.69 Hz (Table 5.1, p. 115). These results indicate that it is possible to obtain reasonable F0 estimates even when the pitch period is nearly of the same duration as the analysis window, on the condition that the appropriate ACC peak-peaking procedure is used. Mark Thesis URL: http://mypage.iu.edu/~mwpennin/GlottalMannerDiss-Pennington.pdf ----------------------------------------------------------------- The "pitch in two cycles" phenomenon is exactly what would be predicted by an autocorrelation model of pitch. With two copies of a pulse, you can measure a consistent interval as a peak in the ACF. Dick Hi list, In many of the papers published by Georg von Békésy he makes the statement that the fundamental frequency was determined by the auditory system "even when the stimulus was only two cycles" in length. In at least one of his publications {The Missing Fundamental and Periodicity Detection in Hearing JASA 1972 512) 631-637) he attributes this to his own experiments and to a paper by Savart.[Annalen der Physik und Chemie 1840 53 ( ) 555-561 in german]. It is quite true that Savart found that the fundamental was determined in two cycles but it was published in an earlier paper by Savart (Ueber die Empfindlichkeit des Gehörorgans Felix Savart Annalen der Physik und Chemie 1830 20( ) 290-304 in german)and no mention of the two cycles is mentioned in the citation by Békésy. Actually from a historical point of view the original paper by Felix Savart was published in French in: Annales de chimie et de Physique 1830 44 ( ) 337-352 in French. Can anyone point me to literature which shows how the auditory system performs the "two cycle" feat, or to papers which show how such a "two cycle" feat might be acomplished mathematically or to any papers of a more recent origin which discusses this ability. Thanks, Fred